Solving Systems of Equations & Inequalities

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What is a system of linear inequalities?

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A set of two or more linear inequalities that involve the same variables.

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What does the solution of a system of linear inequalities represent?

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The set of all points that satisfy all inequalities in the system, often represented as a shaded region on a graph.

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What is the substitution method in solving systems of equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What does it mean if a system of equations has no solution?

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It means that the lines represented by the equations are parallel and never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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It means that the equations represent the same line, and there are an infinite number of points that satisfy both equations.

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How do you graph a linear inequality?

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Graph the corresponding linear equation as a boundary line, then shade the region that satisfies the inequality.

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What is the first step in solving a system of equations using substitution?

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Get either variable by itself in one of the equations.

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What is the significance of the intersection point of two lines in a system of equations?

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It represents the solution to the system, where both equations are satisfied.

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How can you determine if a point is a solution to a system of inequalities?

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Substitute the point into each inequality; if it satisfies all inequalities, it is a solution.